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arXiv · 1911.02706

Einstein and scalar flat Riemannian metrics

Santiago R Simanca
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Abstract

On a given closed connected manifold of dimension two, or greater, we consider the squared $L^2$-norm of the scalar curvature functional over the space of constant volume Riemannian metrics. We prove that its critical points have constant scalar curvature, and use this to show that a metric is a solution of the critical point equation if, and only if, it is either Einstein, or scalar flat.

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Santiago R Simanca. 2019-11-07. Einstein and scalar flat Riemannian metrics. https://arxiv.org/abs/1911.02706

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